Can some one explain me these synthesis reaction

https://docs.google.com/document/d/1-3dR…

The first reaction is the synthesis of tert-butyl methyl ether (TBME), which is added to gasoline as an octane enhancer. Regarding the synthesis, propene abstracts a hydrogen from sulfuric acid to give a propenyl carbocation (carbocation @ C2) and the subsequent attack of methanol to the electropositive center, which would ultimately give a charged tert-butyl methyl ether. The bisulfate would then get the hydrogen attached to methanol to give a neutral TBME product. H2SO4 acted as an acid catalyst in this step.

The second reaction is similar to the first reaction however there is a twist: the methyl shift. The electron rich alkene would attack the hydrogen from HBr to give an intermediate which is 2,2-dimethylbutyl carbocation (carbocation @ C3) and the free bromide ion. Now, the 2,2-dimehtylbutyl carbocation would rearrange via a methyl shift to give a 2,3-dimethylbutyl (carbocation @ C2).

Twist: One methyl group (2,2-dimethylbutyl carbocation) would traverse towards the carbocation at C3. Now the carbocation initially secondary became tertiary, which is a more stable carbocation. The rearranged product is more stable than the former product.

Then the 2,3-dimethylbutyl carbocation is attacked by the bromide ion to give 2-bromo-2,3-dimethylbutane.